Hemodynamics and wall mechanics in human carotid bifurcation and its consequences for atherogenesis: investigation of inter-individual variation.

Finite element simulations of fluid-solid interactions were used to investigate inter-individual variations in flow dynamics and wall mechanics at the carotid artery bifurcation, and its effects on atherogenesis, in three healthy humans (normal volunteers: NV1, NV2, NV4). Subject-specific calculations were based on MR images of structural anatomy and ultrasound measurements of flow at domain boundaries. For all subjects, the largest contiguous region of low wall shear stress (WSS) occurred at the carotid bulb, WSS was high (6-10 Pa) at the apex, and a small localized region of WSS > 10 Pa occurred close to the inner wall of the external carotid artery (ECA). NV2 and NV4 had a "spot" of low WSS distal to the bifurcation at the inner wall of the ECA. Low WSS patches in the common carotid artery (CCA) were contiguous with the carotid bulb low WSS region in NV1 and NV2, but not in NV4. In all three subjects, areas of high oscillatory shear index (OSI) were confined to regions of low WSS. Only NV4 exhibited high levels of OSI on the external adjoining wall of the ECA and CCA. For all subjects, the maximum wall shear stress temporal gradient (WSSTG) was highest at the flow divider (reaching 1,000 Pa/s), exceeding 300 Pa/s at the walls connecting the ECA and CCA, but remaining below 250 Pa/s outside of the ECA. In all subjects, (maximum principle) cyclic strain (CS) was greatest at the apex (NV1: 14%; NV2: 11%; NV4: 6%), and a second high CS region occurred at the ECA-CCA adjoining wall (NV1: 11%, NV2: 9%, NV4: 5%). Wall deformability was included in one simulation (NV2) to verify that it had little influence on the parameters studied. Location and magnitude of low WSS were similar, except for the apex (differences of up to 25%). Wall distensibility also influenced OSI, doubling it in most of the CCA, separating the single high OSI region of the carotid bulb into two smaller regions, and shrinking the ECA internal and external walls' high OSI regions. These observations provide further evidence that significant intra-subject variability exists in those factors thought to impact atherosclerosis.

Characterization of the atherosclerotic carotid bifurcation using MRI, finite element modeling, and histology.

Atherogenesis is known to be associated with the stresses that act on or within the arterial wall. Still, the uneven distribution of atherosclerotic lesions and the impact of vessel remodeling on disease progression are poorly understood. A methodology is proposed to study the correlations between fluid dynamic parameters and histological markers of atherosclerosis. Trends suggested by preliminary data from four patients with advanced carotid bifurcation arterial disease are examined and compared to hypotheses in the literature. Four patients were scanned using MRI and ultrasound, and subsequently underwent carotid endarterectomy. For each patient. a geometric model and a numerical mesh were constructed from MR data, and velocity boundary conditions established. Computations yield values for average wall shear stress (WSS), maximum wall shear stress temporal gradient (WSSTG), and Oscillatory Shear Index (OSI). Following surgery, the excised plaques were sectioned, stained for smooth muscle cells (SMC), macrophages (M phi), lipid (LIP), and collagen (COL), and analyzed quantitatively. Correlations attempted between the various fluid dynamic variables and the biological markers were interesting but inconclusive. Tendencies of WSSTG and WSS to correlate negatively with M phi and LIP, and positively with COL and SMC, as well as tendencies of OSI to correlate positively with Mphi and LIP and negatively with COL and SMC, were observed. These trends agree with hypotheses in the literature, which are based on ex vivo and in vitro experimental studies.

Computational analysis of the effects of exercise on hemodynamics in the carotid bifurcation.

The important influence of hemodynamic factors in the initiation and progression of arterial disease has led to numerous studies to computationally simulate blood flow at sites of disease and examine potential correlative factors. This study considers the differences in hemodynamics produced by varying heart rate in a fully coupled fluid-structure three-dimensional finite element model of a carotid bifurcation. Two cases with a 50% increase in heart rate are considered: one in which peripheral resistance is uniformly reduced to maintain constant mean arterial pressure, resulting in an increase in mean flow, and a second in which cerebral vascular resistance is held constant so that mean carotid artery flow is nearly unchanged. Results show that, with increased flow rate, the flow patterns are relatively unchanged, but the magnitudes of mean and instantaneous wall shear stress are increased roughly in proportion to the flow rate, except at the time of minimum flow (and maximum flow separation) when shear stress in the carotid bulb is increased in magnitude more than threefold. When cerebral peripheral resistance is held constant, the differences are much smaller, except again at end diastole. Maximum wall shear stress temporal gradient is elevated in both cases with elevated heart rate. Changes in oscillatory shear index are minimal. These findings suggest that changes in the local hemodynamics due to mild exercise may be relatively small in the carotid artery.

On the sensitivity of wall stresses in diseased arteries to variable material properties.

Accurate estimates of stress in an atherosclerotic lesion require knowledge of the material properties of its components (e.g., normal wall, fibrous plaque, calcified regions, lipid pools) that can only be approximated. This leads to considerable uncertainty in these computational predictions. A study was conducted to test the sensitivity of predicted levels of stress and strain to the parameter values of plaque used in finite element analysis. Results show that the stresses within the arterial wall, fibrous plaque, calcified plaque, and lipid pool have low sensitivities for variation in the elastic modulus. Even a +/- 50% variation in elastic modulus leads to less than a 10% change in stress at the site of rupture. Sensitivity to variations in elastic modulus is comparable between isotropic nonlinear, isotropic nonlinear with residual strains, and transversely isotropic linear models. Therefore, stress analysis may be used with confidence that uncertainty in the material properties generates relatively small errors in the prediction of wall stresses. Either isotropic nonlinear or anisotropic linear models provide useful estimates, however the predictions in regions of stress concentration (e.g., the site of rupture) are somewhat more sensitive to the specific model used, increasing by up to 30% from the isotropic nonlinear to orthotropic model in the present example. Changes resulting from the introduction of residual stresses are much smaller.